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Illusory bimodality in repeated reconstructions of probability distributions

  • Author(s): Nie, Shaozhi
  • Wang, Muzhi
  • Zhang, Hang
  • et al.
Abstract

Probability density estimation is widely-known as an ill-posed statistical problem whose solving depends on extra constraints. We investigated what prior beliefs people might have in their learning of an arbitrary probability distribution, especially whether the distribution is believed to be unimodal or multimodal. In each block of our experiments, participants repeatedly reconstructed a one-dimensional spatial distribution after observing every 60 new samples from the distribution. The probability distribution function (PDF) they reported on each trial was submitted to a spectral analysis, where the powers for 1-cycle, 2-cycle, …, n-cycle components respectively indicate participants’ tendency of reporting unimodal, bimodal, …, n-modal distributions. In two experiments, the reported PDFs showed significant bimodality—that the 2-cycle power was above chance and even larger than the 1-cycle power—not only for bimodal distributions, but also for uniform distribution. Such illusory bimodality for uniform distribution was first found when we used an adaptive procedure analogous to “human MCMC”, updating the generative distribution of samples from trial to trial to reinforce potential biases in PDFs (Experiment 1). However, even when we fixed the generative distribution across trials (Experiment 2), the illusory bimodality did not vanish. The illusory bimodality was even observed before participants experienced any bimodal distributions in the experiment . We considered a few kernel density models and discuss further computational explanations (e.g. prior beliefs following Chinese Restaurant Process) for this new phenomenon.

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